In many applications a sample of networks, rather than a single instance, is collected, and observations within that sample provide complementary information about the complex system under scrutiny. In the study of connectomics, for example, connectivity networks are collected across various modes - across time, individuals, or cognitive task [1]}, [2]}, [3]}, [4]}. Multi-transit transportation systems involve traffic measurements on the same geographic area across many forms of transportation [5]}, [6]}. An individual's social influence depends on their interactions across a collection of social media platforms rather than just a single platform [7]}. In applications like these, relational data are collected as a sample of networks \(\mathbf {G}_N := \lbrace G_1, \ldots , G_N\rbrace \) , where observation \(i\)  is represented by the network \(G_i = (V_i, E_i)\)  with vertex set \(V_i\)  and edge set \(E_i\) . Despite the increasing prominence of network samples arising in nature, the tools available for analyzing network samples remain limited.
